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<h1>Numeric Types</h1>
</td>
</tr>
</table>
<ul class="minitoc">
<li>
<a href="#Numeric+Type+Overview">Numeric Type Overview</a>
</li>
<li>
<a href="#Numeric+Type+Promotion+in+Expressions">Numeric Type Promotion in Expressions</a>
</li>
<li>
<a href="#Storing+Values+of+One+Numeric+Data+Type+in+Columns+of+Another+Numeric+Data+Type">Storing Values of One Numeric Data Type in Columns of Another Numeric Data Type</a>
</li>
<li>
<a href="#Scale+for+Decimal+Arithmetic">Scale for Decimal Arithmetic</a>
</li>
</ul>
<a name="N10043"></a><a name="Numeric+Type+Overview"></a>
<h3>Numeric Type Overview</h3>
<div style="margin-left: 0 ; border: 2px">
<p>Numeric types include the following types, which provide storage of varying sizes:</p>
<ul>
<li>Integer numerics <ul>
<li>
<a href="sqlj141.html#HDRSII-SQLJ-16221">SMALLINT</a> (2 bytes)</li>
<li>
<a href="sqlj136.html#HDRSII-SQLJ-10696">INTEGER</a> (4 bytes)</li>
<li>
<a href="sqlj126.html#HDRSII-SQLJ-30435">BIGINT</a> (8 bytes)</li>
</ul>
</li>
<li>Approximate or floating-point numerics <ul>
<li>
<a href="sqlj140.html#HDRSII-SQLJ-14122">REAL</a> (4 bytes)</li>
<li>
<a href="sqlj134.html#SPTSII-SQLJ-DOUBLEPRECISION">DOUBLE PRECISION</a> (8 bytes)</li>
<li>
<a href="sqlj135.html#HDRSII-SQLJ-27281">FLOAT</a> (an alias for <a href="sqlj134.html#SPTSII-SQLJ-DOUBLEPRECISION">DOUBLE PRECISION</a> or <a href="sqlj140.html#HDRSII-SQLJ-14122">REAL</a>)</li>
</ul>
</li>
<li>Exact numeric <ul>
<li>
<a href="sqlj132.html#HDRSII-SQLJ-15260">DECIMAL</a> (storage based on precision)</li>
<li>
<a href="sqlj139.html#HDRSII-SQLJ-12362">NUMERIC</a> (an alias for <a href="sqlj132.html#HDRSII-SQLJ-15260">DECIMAL</a>)</li>
</ul>
</li>
</ul>
</div>
<a name="N10087"></a><a name="Numeric+Type+Promotion+in+Expressions"></a>
<h3>Numeric Type Promotion in Expressions</h3>
<div style="margin-left: 0 ; border: 2px">
<p>In expressions that use only integer types, Derby promotes the type of the result to at least INTEGER. In expressions that mix integer with non-integer types, Derby promotes the result of the expression to the highest type in the expression. <a href="#TBLSII-SQLJ-39640">Table 4</a> shows the promotion of data types in expressions.<br>
</p>
<p>
<strong>Table 4. Type Promotion in Expressions</strong>
<br>
</p>
<table class="ForrestTable" cellspacing="1" cellpadding="4">
<tr>
<th><a name="WQ32"></a>Largest Type That Appears in Expression</th><th><a name="WQ33"></a>Resulting Type of Expression</th>
</tr>
<tr>
<td headers="WQ32" width="62%">DOUBLE PRECISION</td><td headers="WQ33" width="38%">DOUBLE PRECISION</td>
</tr>
<tr>
<td headers="WQ32" width="62%">REAL</td><td headers="WQ33" width="38%">DOUBLE PRECISION</td>
</tr>
<tr>
<td headers="WQ32" width="62%">DECIMAL</td><td headers="WQ33" width="38%">DECIMAL</td>
</tr>
<tr>
<td headers="WQ32" width="62%">BIGINT</td><td headers="WQ33" width="38%">BIGINT</td>
</tr>
<tr>
<td headers="WQ32" width="62%">INTEGER</td><td headers="WQ33" width="38%">INTEGER</td>
</tr>
<tr>
<td headers="WQ32" width="62%">SMALLINT</td><td headers="WQ33" width="38%">INTEGER</td>
</tr>
</table>
<p>For example:</p>
<pre>
<strong>-- returns a double precision 
VALUES 1 + 1.0e0
 -- returns a decimal 
VALUES 1 + 1.0
 -- returns an integer 
VALUES CAST (1 AS INT) + CAST (1 AS INT)</strong>

</pre>
</div>
<a name="N100DC"></a><a name="Storing+Values+of+One+Numeric+Data+Type+in+Columns+of+Another+Numeric+Data+Type"></a>
<h3>Storing Values of One Numeric Data Type in Columns of Another Numeric Data Type</h3>
<div style="margin-left: 0 ; border: 2px">
<p>An attempt to put a floating-point type of a larger storage size into a location of a smaller size fails only if the value cannot be stored in the smaller-size location. For example:</p>
<pre>
<strong>create table mytable (r REAL, d DOUBLE PRECISION);</strong>
0 rows inserted/updated/deleted
<strong>INSERT INTO mytable (r, d) values (3.4028236E38, 3.4028235E38);</strong>
ERROR X0X41: The number '3.4028236E38' is outside the range for
the data type REAL.
</pre>
<p>You can store a floating point type in an INTEGER column; the fractional part of the number is truncated. For example:</p>
<pre>
<strong>INSERT INTO mytable(integer_column) values (1.09e0); 
1 row inserted/updated/deleted
 SELECT integer_column
FROM mytable; 
I
---------------
1</strong>

</pre>
<p>Integer types can always be placed successfully in approximate numeric values, although with the possible loss of some precision.</p>
<p>Integers can be stored in decimals if the DECIMAL precision is large enough for the value. For example:</p>
<pre>
<strong>ij&gt;  insert into mytable (decimal_column)
VALUES (55555555556666666666); 
ERROR X0Y21: The number '55555555556666666666' is outside the
range of the target DECIMAL/NUMERIC(5,2) datatype.</strong>

</pre>
<p>An attempt to put an integer value of a larger storage size into a location of a smaller size fails if the value cannot be stored in the smaller-size location. For example:</p>
<pre>
<strong>INSERT INTO mytable (int_column) values 2147483648; 
ERROR 22003: The resulting value is outside the range for the 
data type INTEGER.</strong>

</pre>
<dl>
<dt>
<strong>Note:</strong>
</dt>
<dd>When truncating trailing digits from a NUMERIC value, Derby rounds down.</dd>
</dl>
</div>
<a name="N10103"></a><a name="Scale+for+Decimal+Arithmetic"></a>
<h3>Scale for Decimal Arithmetic</h3>
<div style="margin-left: 0 ; border: 2px">
<p>
<a name="IDX992"></a>  SQL statements can involve arithmetic expressions that use decimal data types of different <em>precision</em>s (the total number of digits, both to the left and to the right of the decimal point) and <em>scale</em>s (the number of digits of the fractional component). The precision and scale of the resulting decimal type depend on the precision and scale of the operands.</p>
<p>Given an arithmetic expression that involves two decimal operands:</p>
<ul>
<li>
<em>lp</em> stands for the precision of the left operand</li>
<li>
<em>rp</em> stands for the precision of the right operand</li>
<li>
<em>ls</em> stands for the scale of the left operand</li>
<li>
<em>rs</em> stands for the scale of the right operand</li>
</ul>
<p>Use the following formulas to determine the scale of the resulting data type for the following kinds of arithmetical expressions:</p>
<ul>
<li>
<em>multiplication</em> 
<p>ls + rs</p>
</li>
<li>
<em>division</em> 
<p>31 - lp + ls - rs</p>
</li>
<li>
<em>AVG()</em> 
<p>max(max(ls, rs), 4)</p>
</li>
<li>
<em>all others</em> 
<p>max(ls, rs)</p>
</li>
</ul>
<p>For example, the scale of the resulting data type of the following expression is 27:</p>
<pre>11.0/1111.33
<strong>// 31 - 3 + 1 - 2 = 27</strong> 

</pre>
<p>Use the following formulas to determine the precision of the resulting data type for the following kinds of arithmetical expressions:</p>
<ul>
<li>
<em>multiplication</em> 
<p>lp + rp</p>
</li>
<li>
<em>addition</em> 
<p>2 * (p - s) + s</p>
</li>
<li>
<em>division</em> 
<p>lp - ls + rp + max(ls + rp - rs + 1, 4)</p>
</li>
<li>
<em>all others</em> 
<p>max(lp - ls, rp - rs) + 1 + max(ls, rs)</p>
</li>
</ul>
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